Abstract

A theoretical framework for the temporal behavior of photoinduced anisotropy in liquid-crystalline azobenzene side-chain polyesters is constructed. The domain structure of the material is taken into account and intermolecular interactions are included through a mean-field description. Photoinduced transcis isomerization is taken as the dominating source of chromophore reorientation events, and it is demonstrated how this mechanism in conjunction with the multidomain picture is able to account for the long-term stability of the anisotropy. The photoinduced birefringence is calculated by means of a truncated basis method, and in addition the photostationary solution is obtained. Comparison between theory and experiment shows excellent agreement in the entire range of intensities used experimentally.

© 1998 Optical Society of America

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  1. M. Eich, J. H. Wendorff, B. Reck, and H. Ringsdorf, “Reversible digital and holographic optical storage in polymeric liquid crystals,” Makromol. Chem., Rapid Commun. 8, 59 (1987).
    [CrossRef]
  2. K. Anderle, R. Birenheide, M. Eich, and J. H. Wendorff, “Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers,” Makromol. Chem., Rapid Commun. 10, 477 (1989).
    [CrossRef]
  3. M. Eich and J. H. Wendorff, “Laser-induced gratings and spectroscopy in monodomains of liquid-crystalline polymers,” J. Opt. Soc. Am. B 7, 1428 (1990).
    [CrossRef]
  4. U. Wiesner, M. Antonietti, C. Boeffel, and H. W. Spiess, “Dynamics of photoinduced isomerization of azobenzene moieties in liquid-crystalline polymers,” Makromol. Chem. 191, 2133 (1990).
    [CrossRef]
  5. U. Wiesner, N. Reynolds, C. Boeffel, and H. W. Spiess, “Photoinduced reorientation in liquid-crystalline polymers below the glass transition temperature studied by time-dependent infrared spectroscopy,” Makromol. Chem., Rapid Commun. 12, 457 (1991).
    [CrossRef]
  6. K. Anderle, R. Birenheide, M. J. A. Werner, and J. H. Wendorff, “Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers,” Liq. Cryst. 9, 691 (1991).
    [CrossRef]
  7. A. Natansohn, P. Rochon, J. Gosselin, and S. Xie, “Azo polymers for reversible optical storage. 1,” Macromolecules 25, 2268 (1992).
    [CrossRef]
  8. S. Hvilsted, F. Andruzzi, and P. S. Ramanujam, “Side-chain liquid-crystalline polyesters for optical information storage,” Opt. Lett. 17, 1234 (1992).
    [CrossRef] [PubMed]
  9. C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
    [CrossRef]
  10. S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
    [CrossRef]
  11. P. S. Ramanujam, S. Hvilsted, I. Zebger, and H. W. Siesler, “On the explanation of the biphotonic processes in polyesters containing azobenzene in the side chain,” Macromol. Rapid Commun. 16, 455 (1995).
    [CrossRef]
  12. N. C. R. Holme, P. S. Ramanujam, and S. Hvilsted, “Photoinduced anisotropy measurements in liquid-crystalline side-chain polyesters,” Appl. Opt. 35, 4622 (1996).
    [CrossRef] [PubMed]
  13. P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
    [CrossRef]
  14. R. Birenheide and J. H. Wendorff, “Anisotropic polymers with photostationary molecules: theoretical approach and practical applications,” in Photopolymer Device Physics, Chemistry and Applications, Proc. SPIE 1213, 210 (1990).
    [CrossRef]
  15. M. Dumont and Z. Sekkat, “Dynamical study of photoinduced anisotropy and orientational relaxation of azo dyes in polymeric films. Poling at room temperature,” in Nonconducting Photopolymers and Applications, Proc. SPIE 1774, 188 (1992).
    [CrossRef]
  16. M. Dumont, G. Froc, and S. Hosotte, “Alignment and orientation of chromophores by optical pumping,” Nonlinear Opt. 9, 327 (1995).
  17. S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).
  18. S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
    [CrossRef]
  19. S. P. Palto and G. Durand, “Friction model of photo-induced reorientation of optical axis in photo-oriented Langmuir-Blodgett films,” J. Phys. II 5, 963 (1995).
  20. T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
    [CrossRef]
  21. T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
    [CrossRef]
  22. T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
    [CrossRef]
  23. W. Maier and A. Saupe, “Eine einfache molekular-statistiche theorie der nematichen kristallinflüssigen phase. Teil I,” Z. Naturforsch. 14a, 882 (1959).
  24. R. Loudon, The Quantum Theory of Light (Oxford University, London, 1991).
  25. R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
    [CrossRef]
  26. N. C. R. Holme, Optics and Fluid Dynamics Department, Risø National Laboratory, Denmark (personal communication, 1997).

1996 (2)

N. C. R. Holme, P. S. Ramanujam, and S. Hvilsted, “Photoinduced anisotropy measurements in liquid-crystalline side-chain polyesters,” Appl. Opt. 35, 4622 (1996).
[CrossRef] [PubMed]

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

1995 (5)

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
[CrossRef]

P. S. Ramanujam, S. Hvilsted, I. Zebger, and H. W. Siesler, “On the explanation of the biphotonic processes in polyesters containing azobenzene in the side chain,” Macromol. Rapid Commun. 16, 455 (1995).
[CrossRef]

M. Dumont, G. Froc, and S. Hosotte, “Alignment and orientation of chromophores by optical pumping,” Nonlinear Opt. 9, 327 (1995).

S. P. Palto and G. Durand, “Friction model of photo-induced reorientation of optical axis in photo-oriented Langmuir-Blodgett films,” J. Phys. II 5, 963 (1995).

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

1994 (1)

C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
[CrossRef]

1993 (2)

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
[CrossRef]

1992 (4)

M. Dumont and Z. Sekkat, “Dynamical study of photoinduced anisotropy and orientational relaxation of azo dyes in polymeric films. Poling at room temperature,” in Nonconducting Photopolymers and Applications, Proc. SPIE 1774, 188 (1992).
[CrossRef]

S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).

A. Natansohn, P. Rochon, J. Gosselin, and S. Xie, “Azo polymers for reversible optical storage. 1,” Macromolecules 25, 2268 (1992).
[CrossRef]

S. Hvilsted, F. Andruzzi, and P. S. Ramanujam, “Side-chain liquid-crystalline polyesters for optical information storage,” Opt. Lett. 17, 1234 (1992).
[CrossRef] [PubMed]

1991 (2)

U. Wiesner, N. Reynolds, C. Boeffel, and H. W. Spiess, “Photoinduced reorientation in liquid-crystalline polymers below the glass transition temperature studied by time-dependent infrared spectroscopy,” Makromol. Chem., Rapid Commun. 12, 457 (1991).
[CrossRef]

K. Anderle, R. Birenheide, M. J. A. Werner, and J. H. Wendorff, “Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers,” Liq. Cryst. 9, 691 (1991).
[CrossRef]

1990 (5)

M. Eich and J. H. Wendorff, “Laser-induced gratings and spectroscopy in monodomains of liquid-crystalline polymers,” J. Opt. Soc. Am. B 7, 1428 (1990).
[CrossRef]

U. Wiesner, M. Antonietti, C. Boeffel, and H. W. Spiess, “Dynamics of photoinduced isomerization of azobenzene moieties in liquid-crystalline polymers,” Makromol. Chem. 191, 2133 (1990).
[CrossRef]

R. Birenheide and J. H. Wendorff, “Anisotropic polymers with photostationary molecules: theoretical approach and practical applications,” in Photopolymer Device Physics, Chemistry and Applications, Proc. SPIE 1213, 210 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
[CrossRef]

1989 (1)

K. Anderle, R. Birenheide, M. Eich, and J. H. Wendorff, “Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers,” Makromol. Chem., Rapid Commun. 10, 477 (1989).
[CrossRef]

1987 (1)

M. Eich, J. H. Wendorff, B. Reck, and H. Ringsdorf, “Reversible digital and holographic optical storage in polymeric liquid crystals,” Makromol. Chem., Rapid Commun. 8, 59 (1987).
[CrossRef]

1959 (1)

W. Maier and A. Saupe, “Eine einfache molekular-statistiche theorie der nematichen kristallinflüssigen phase. Teil I,” Z. Naturforsch. 14a, 882 (1959).

Anderle, K.

K. Anderle, R. Birenheide, M. J. A. Werner, and J. H. Wendorff, “Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers,” Liq. Cryst. 9, 691 (1991).
[CrossRef]

K. Anderle, R. Birenheide, M. Eich, and J. H. Wendorff, “Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers,” Makromol. Chem., Rapid Commun. 10, 477 (1989).
[CrossRef]

Andruzzi, F.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
[CrossRef]

S. Hvilsted, F. Andruzzi, and P. S. Ramanujam, “Side-chain liquid-crystalline polyesters for optical information storage,” Opt. Lett. 17, 1234 (1992).
[CrossRef] [PubMed]

Antonietti, M.

U. Wiesner, M. Antonietti, C. Boeffel, and H. W. Spiess, “Dynamics of photoinduced isomerization of azobenzene moieties in liquid-crystalline polymers,” Makromol. Chem. 191, 2133 (1990).
[CrossRef]

Birenheide, R.

K. Anderle, R. Birenheide, M. J. A. Werner, and J. H. Wendorff, “Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers,” Liq. Cryst. 9, 691 (1991).
[CrossRef]

R. Birenheide and J. H. Wendorff, “Anisotropic polymers with photostationary molecules: theoretical approach and practical applications,” in Photopolymer Device Physics, Chemistry and Applications, Proc. SPIE 1213, 210 (1990).
[CrossRef]

K. Anderle, R. Birenheide, M. Eich, and J. H. Wendorff, “Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers,” Makromol. Chem., Rapid Commun. 10, 477 (1989).
[CrossRef]

Blinov, L. M.

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).

Boeffel, C.

U. Wiesner, N. Reynolds, C. Boeffel, and H. W. Spiess, “Photoinduced reorientation in liquid-crystalline polymers below the glass transition temperature studied by time-dependent infrared spectroscopy,” Makromol. Chem., Rapid Commun. 12, 457 (1991).
[CrossRef]

U. Wiesner, M. Antonietti, C. Boeffel, and H. W. Spiess, “Dynamics of photoinduced isomerization of azobenzene moieties in liquid-crystalline polymers,” Makromol. Chem. 191, 2133 (1990).
[CrossRef]

Delaire, J. A.

R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
[CrossRef]

Doke, Y.

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

Dumont, M.

M. Dumont, G. Froc, and S. Hosotte, “Alignment and orientation of chromophores by optical pumping,” Nonlinear Opt. 9, 327 (1995).

R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
[CrossRef]

M. Dumont and Z. Sekkat, “Dynamical study of photoinduced anisotropy and orientational relaxation of azo dyes in polymeric films. Poling at room temperature,” in Nonconducting Photopolymers and Applications, Proc. SPIE 1774, 188 (1992).
[CrossRef]

Durand, G.

S. P. Palto and G. Durand, “Friction model of photo-induced reorientation of optical axis in photo-oriented Langmuir-Blodgett films,” J. Phys. II 5, 963 (1995).

Eich, M.

M. Eich and J. H. Wendorff, “Laser-induced gratings and spectroscopy in monodomains of liquid-crystalline polymers,” J. Opt. Soc. Am. B 7, 1428 (1990).
[CrossRef]

K. Anderle, R. Birenheide, M. Eich, and J. H. Wendorff, “Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers,” Makromol. Chem., Rapid Commun. 10, 477 (1989).
[CrossRef]

M. Eich, J. H. Wendorff, B. Reck, and H. Ringsdorf, “Reversible digital and holographic optical storage in polymeric liquid crystals,” Makromol. Chem., Rapid Commun. 8, 59 (1987).
[CrossRef]

Froc, G.

M. Dumont, G. Froc, and S. Hosotte, “Alignment and orientation of chromophores by optical pumping,” Nonlinear Opt. 9, 327 (1995).

Gosselin, J.

A. Natansohn, P. Rochon, J. Gosselin, and S. Xie, “Azo polymers for reversible optical storage. 1,” Macromolecules 25, 2268 (1992).
[CrossRef]

Grewer, G.

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

Hayashi, T.

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

Hoffman, U.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

Holme, C.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

Holme, N. C. R.

Horiuchi, S.

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
[CrossRef]

Hosotte, S.

M. Dumont, G. Froc, and S. Hosotte, “Alignment and orientation of chromophores by optical pumping,” Nonlinear Opt. 9, 327 (1995).

Hvilsted, S.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

N. C. R. Holme, P. S. Ramanujam, and S. Hvilsted, “Photoinduced anisotropy measurements in liquid-crystalline side-chain polyesters,” Appl. Opt. 35, 4622 (1996).
[CrossRef] [PubMed]

P. S. Ramanujam, S. Hvilsted, I. Zebger, and H. W. Siesler, “On the explanation of the biphotonic processes in polyesters containing azobenzene in the side chain,” Macromol. Rapid Commun. 16, 455 (1995).
[CrossRef]

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
[CrossRef]

C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
[CrossRef]

S. Hvilsted, F. Andruzzi, and P. S. Ramanujam, “Side-chain liquid-crystalline polyesters for optical information storage,” Opt. Lett. 17, 1234 (1992).
[CrossRef] [PubMed]

Ikeda, T.

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
[CrossRef]

Karanjit, D. B.

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
[CrossRef]

Kawakami, H.

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

Khavrichev, V. A.

S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).

Kulinna, C.

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
[CrossRef]

C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
[CrossRef]

Kurihara, S.

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
[CrossRef]

Lösche, M.

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

Loucif-Saïbi, R.

R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
[CrossRef]

Magagnini, P.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

Maier, W.

W. Maier and A. Saupe, “Eine einfache molekular-statistiche theorie der nematichen kristallinflüssigen phase. Teil I,” Z. Naturforsch. 14a, 882 (1959).

Nakatani, K.

R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
[CrossRef]

Natansohn, A.

A. Natansohn, P. Rochon, J. Gosselin, and S. Xie, “Azo polymers for reversible optical storage. 1,” Macromolecules 25, 2268 (1992).
[CrossRef]

Onogi, Y.

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

Paci, M.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

Palto, S. P.

S. P. Palto and G. Durand, “Friction model of photo-induced reorientation of optical axis in photo-oriented Langmuir-Blodgett films,” J. Phys. II 5, 963 (1995).

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).

Pedersen, M.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

Ramanujam, P. S.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

N. C. R. Holme, P. S. Ramanujam, and S. Hvilsted, “Photoinduced anisotropy measurements in liquid-crystalline side-chain polyesters,” Appl. Opt. 35, 4622 (1996).
[CrossRef] [PubMed]

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
[CrossRef]

P. S. Ramanujam, S. Hvilsted, I. Zebger, and H. W. Siesler, “On the explanation of the biphotonic processes in polyesters containing azobenzene in the side chain,” Macromol. Rapid Commun. 16, 455 (1995).
[CrossRef]

C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
[CrossRef]

S. Hvilsted, F. Andruzzi, and P. S. Ramanujam, “Side-chain liquid-crystalline polyesters for optical information storage,” Opt. Lett. 17, 1234 (1992).
[CrossRef] [PubMed]

Reck, B.

M. Eich, J. H. Wendorff, B. Reck, and H. Ringsdorf, “Reversible digital and holographic optical storage in polymeric liquid crystals,” Makromol. Chem., Rapid Commun. 8, 59 (1987).
[CrossRef]

Reynolds, N.

U. Wiesner, N. Reynolds, C. Boeffel, and H. W. Spiess, “Photoinduced reorientation in liquid-crystalline polymers below the glass transition temperature studied by time-dependent infrared spectroscopy,” Makromol. Chem., Rapid Commun. 12, 457 (1991).
[CrossRef]

Ringsdorf, H.

M. Eich, J. H. Wendorff, B. Reck, and H. Ringsdorf, “Reversible digital and holographic optical storage in polymeric liquid crystals,” Makromol. Chem., Rapid Commun. 8, 59 (1987).
[CrossRef]

Rochon, P.

A. Natansohn, P. Rochon, J. Gosselin, and S. Xie, “Azo polymers for reversible optical storage. 1,” Macromolecules 25, 2268 (1992).
[CrossRef]

Saupe, A.

W. Maier and A. Saupe, “Eine einfache molekular-statistiche theorie der nematichen kristallinflüssigen phase. Teil I,” Z. Naturforsch. 14a, 882 (1959).

Schönhoff, M.

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

Sekkat, Z.

R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
[CrossRef]

M. Dumont and Z. Sekkat, “Dynamical study of photoinduced anisotropy and orientational relaxation of azo dyes in polymeric films. Poling at room temperature,” in Nonconducting Photopolymers and Applications, Proc. SPIE 1774, 188 (1992).
[CrossRef]

Siesler, H. W.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
[CrossRef]

P. S. Ramanujam, S. Hvilsted, I. Zebger, and H. W. Siesler, “On the explanation of the biphotonic processes in polyesters containing azobenzene in the side chain,” Macromol. Rapid Commun. 16, 455 (1995).
[CrossRef]

C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
[CrossRef]

Spiess, H. W.

U. Wiesner, N. Reynolds, C. Boeffel, and H. W. Spiess, “Photoinduced reorientation in liquid-crystalline polymers below the glass transition temperature studied by time-dependent infrared spectroscopy,” Makromol. Chem., Rapid Commun. 12, 457 (1991).
[CrossRef]

U. Wiesner, M. Antonietti, C. Boeffel, and H. W. Spiess, “Dynamics of photoinduced isomerization of azobenzene moieties in liquid-crystalline polymers,” Makromol. Chem. 191, 2133 (1990).
[CrossRef]

Tassi, E. L.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

Tazuke, S.

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
[CrossRef]

Tsuchida, A.

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

Udal’yev, A. A.

S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).

Wendorff, J. H.

K. Anderle, R. Birenheide, M. J. A. Werner, and J. H. Wendorff, “Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers,” Liq. Cryst. 9, 691 (1991).
[CrossRef]

R. Birenheide and J. H. Wendorff, “Anisotropic polymers with photostationary molecules: theoretical approach and practical applications,” in Photopolymer Device Physics, Chemistry and Applications, Proc. SPIE 1213, 210 (1990).
[CrossRef]

M. Eich and J. H. Wendorff, “Laser-induced gratings and spectroscopy in monodomains of liquid-crystalline polymers,” J. Opt. Soc. Am. B 7, 1428 (1990).
[CrossRef]

K. Anderle, R. Birenheide, M. Eich, and J. H. Wendorff, “Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers,” Makromol. Chem., Rapid Commun. 10, 477 (1989).
[CrossRef]

M. Eich, J. H. Wendorff, B. Reck, and H. Ringsdorf, “Reversible digital and holographic optical storage in polymeric liquid crystals,” Makromol. Chem., Rapid Commun. 8, 59 (1987).
[CrossRef]

Werner, M. J. A.

K. Anderle, R. Birenheide, M. J. A. Werner, and J. H. Wendorff, “Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers,” Liq. Cryst. 9, 691 (1991).
[CrossRef]

Wiesner, U.

U. Wiesner, N. Reynolds, C. Boeffel, and H. W. Spiess, “Photoinduced reorientation in liquid-crystalline polymers below the glass transition temperature studied by time-dependent infrared spectroscopy,” Makromol. Chem., Rapid Commun. 12, 457 (1991).
[CrossRef]

U. Wiesner, M. Antonietti, C. Boeffel, and H. W. Spiess, “Dynamics of photoinduced isomerization of azobenzene moieties in liquid-crystalline polymers,” Makromol. Chem. 191, 2133 (1990).
[CrossRef]

Xie, S.

A. Natansohn, P. Rochon, J. Gosselin, and S. Xie, “Azo polymers for reversible optical storage. 1,” Macromolecules 25, 2268 (1992).
[CrossRef]

Yamamoto, M.

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

Yudin, S. G.

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).

Zebger, I.

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

P. S. Ramanujam, S. Hvilsted, I. Zebger, and H. W. Siesler, “On the explanation of the biphotonic processes in polyesters containing azobenzene in the side chain,” Macromol. Rapid Commun. 16, 455 (1995).
[CrossRef]

C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
[CrossRef]

Appl. Opt. (1)

Chem. Mater. (1)

R. Loucif-Saïbi, K. Nakatani, J. A. Delaire, M. Dumont, and Z. Sekkat, “Photoisomerization and second harmonic generation in Disperse Red One-doped and-functionalized Poly(methyl methacrylate) films,” Chem. Mater. 5, 229 (1993).
[CrossRef]

Chem. Phys. Lett. (1)

S. P. Palto, L. M. Blinov, S. G. Yudin, G. Grewer, M. Schönhoff, and M. Lösche, “Photoinduced optical anisotropy in organic molecular films controlled by an electric field,” Chem. Phys. Lett. 202, 308 (1993).
[CrossRef]

Eur. Polym. J. (1)

T. Hayashi, H. Kawakami, Y. Doke, A. Tsuchida, Y. Onogi, and M. Yamamoto, “Photo-induced phase transition of side chain liquid crystalline copolymers with photochromic group,” Eur. Polym. J. 31, 23 (1995).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. II (1)

S. P. Palto and G. Durand, “Friction model of photo-induced reorientation of optical axis in photo-oriented Langmuir-Blodgett films,” J. Phys. II 5, 963 (1995).

Liq. Cryst. (1)

K. Anderle, R. Birenheide, M. J. A. Werner, and J. H. Wendorff, “Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers,” Liq. Cryst. 9, 691 (1991).
[CrossRef]

Macromol. Rapid Commun. (1)

P. S. Ramanujam, S. Hvilsted, I. Zebger, and H. W. Siesler, “On the explanation of the biphotonic processes in polyesters containing azobenzene in the side chain,” Macromol. Rapid Commun. 16, 455 (1995).
[CrossRef]

Macromol. Symp. (1)

C. Kulinna, I. Zebger, S. Hvilsted, P. S. Ramanujam, and H. W. Siesler, “Characterization of the segmental mobility of liquid-crystalline side-chain polyesters by Fourier-transform infrared spectroscopy,” Macromol. Symp. 83, 169 (1994).
[CrossRef]

Macromolecules (4)

S. Hvilsted, F. Andruzzi, C. Kulinna, H. W. Siesler, and P. S. Ramanujam, “Novel side-chain liquid crystalline polyester architecture for reversible optical storage,” Macromolecules 28, 2172 (1995).
[CrossRef]

A. Natansohn, P. Rochon, J. Gosselin, and S. Xie, “Azo polymers for reversible optical storage. 1,” Macromolecules 25, 2268 (1992).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 1. Calorimetric studies and order parameters,” Macromolecules 23, 36 (1990).
[CrossRef]

T. Ikeda, S. Horiuchi, D. B. Karanjit, S. Kurihara, and S. Tazuke, “Photochemically induced isothermal phase transition in polymer liquid crystals with mesogenic phenyl benzoate side chains. 2. Photochemically induced isothermal phase transition behaviors,” Macromolecules 23, 42 (1990).
[CrossRef]

Makromol. Chem. (1)

U. Wiesner, M. Antonietti, C. Boeffel, and H. W. Spiess, “Dynamics of photoinduced isomerization of azobenzene moieties in liquid-crystalline polymers,” Makromol. Chem. 191, 2133 (1990).
[CrossRef]

Makromol. Chem., Rapid Commun. (3)

U. Wiesner, N. Reynolds, C. Boeffel, and H. W. Spiess, “Photoinduced reorientation in liquid-crystalline polymers below the glass transition temperature studied by time-dependent infrared spectroscopy,” Makromol. Chem., Rapid Commun. 12, 457 (1991).
[CrossRef]

M. Eich, J. H. Wendorff, B. Reck, and H. Ringsdorf, “Reversible digital and holographic optical storage in polymeric liquid crystals,” Makromol. Chem., Rapid Commun. 8, 59 (1987).
[CrossRef]

K. Anderle, R. Birenheide, M. Eich, and J. H. Wendorff, “Laser-induced reorientation of the optical axis in liquid-crystalline side chain polymers,” Makromol. Chem., Rapid Commun. 10, 477 (1989).
[CrossRef]

Mol. Mater. (1)

S. P. Palto, V. A. Khavrichev, S. G. Yudin, L. M. Blinov, and A. A. Udal’yev, “On a model of photoinduced optical anisotropy in Langmuir–Blodgett films: low temperature studies,” Mol. Mater. 2, 63 (1992).

Nonlinear Opt. (1)

M. Dumont, G. Froc, and S. Hosotte, “Alignment and orientation of chromophores by optical pumping,” Nonlinear Opt. 9, 327 (1995).

Opt. Lett. (1)

Polym. Adv. Tech. (1)

P. S. Ramanujam, C. Holme, S. Hvilsted, M. Pedersen, F. Andruzzi, M. Paci, E. L. Tassi, P. Magagnini, U. Hoffman, I. Zebger, and H. W. Siesler, “Side-chain liquid crystalline polyesters for optical information storage,” Polym. Adv. Tech. 7, 768 (1996).
[CrossRef]

Proc. SPIE (2)

R. Birenheide and J. H. Wendorff, “Anisotropic polymers with photostationary molecules: theoretical approach and practical applications,” in Photopolymer Device Physics, Chemistry and Applications, Proc. SPIE 1213, 210 (1990).
[CrossRef]

M. Dumont and Z. Sekkat, “Dynamical study of photoinduced anisotropy and orientational relaxation of azo dyes in polymeric films. Poling at room temperature,” in Nonconducting Photopolymers and Applications, Proc. SPIE 1774, 188 (1992).
[CrossRef]

Z. Naturforsch. (1)

W. Maier and A. Saupe, “Eine einfache molekular-statistiche theorie der nematichen kristallinflüssigen phase. Teil I,” Z. Naturforsch. 14a, 882 (1959).

Other (2)

R. Loudon, The Quantum Theory of Light (Oxford University, London, 1991).

N. C. R. Holme, Optics and Fluid Dynamics Department, Risø National Laboratory, Denmark (personal communication, 1997).

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Figures (5)

Fig. 1
Fig. 1

Illustration of the geometry used for describing the temporal evolution of the angular distribution of chromophores. The coordinate system is defined by the polarization vector of the writing beam ε and the initial director.

Fig. 2
Fig. 2

Phase diagram for a domain described by the Maier–Saupe mean-field potential. The various transcendental solutions for the initial order parameter S0 are shown as a function of the inverse temperature c01/T. An ordered (nematic) phase and a disordered (isotropic) phase can be identified, and it is seen that these phases are coexisting for 6.73c07.5.

Fig. 3
Fig. 3

Experimental intensity dependence of the initial slope of the recorded phase difference. From the fit (solid curve) it is seen that the data is well described by a linear dependence.

Fig. 4
Fig. 4

Comparison between the experimental phase difference (solid curve) and the theoretical prediction (dashed curve) from Eq. (55). The error is of the order of 5% for the entire range of writing intensities used experimentally.

Fig. 5
Fig. 5

Calculation of the photostationary birefringence Δn as a function of the writing intensity. The vertical dashed line indicates the threshold intensity Ith, below which the domain directors are frozen.

Tables (1)

Tables Icon

Table 1 Fitting Parameters

Equations (70)

Equations on this page are rendered with MathJax. Learn more.

[fT(θ, φ)+fC(θ, φ)]dΩ=1,
ddt fT(θ, φ)=ACTIp(θ, φ)fC(θ, φ)cos2 θdΩ
-ATCIfT(θ, φ)cos2 θ+1τ [NTp(θ, φ)-fT(θ, φ)],
ddt fC(θ, φ)=ATCIp(θ, φ)fT(θ, φ)cos2 θdΩ
-ACTIfC(θ, φ)cos2 θ+1τ [NCp(θ, φ)-fC(θ, φ)].
ACT=1ω σCTϕCT,
fX(θ)=02πfX(θ, φ)dφ,X=T, C,
p(θ)=02πp(θ, φ)dφ.
ddt fT(θ)=ACTIp(θ)0πfC(θ)cos2 θ sin θdθ-ATCIfT(θ)cos2 θ+1τ [NTp(θ)-fT(θ)],
ddt fC(θ)=ATCIp(θ)0πfT(θ)cos2 θ sin θdθ-ACTIfC(θ)cos2 θ+1τ [NCp(θ)-fC(θ)].
fT(θ)=n=0anP2n(cos θ),
fC(θ)=n=0bnP2n(cos θ),
a˙n=ACTIΓn23 b0+415 b1-ATCI{αnan-1+βnan+γnan+1}+1τ {2a0Γn-an},
b˙n=ATCIΓn23 a0+415 a1-ACTI{αnbn-1+βnbn+γnbn+1}+1τ {2b0Γn-bn},
αn=(2n-1)2n(4n-3)(4n-1),
βn=8n2+4n-1(4n-1)(4n+3),
γn=(2n+1)(2n+2)(4n+3)(4n+5),
Γn=4n+12 02π0πp(θ, φ)P2n(cos θ)sinθ dθdφ.
x2P2n(x)=4n-34n+1 αnP2n-2(x)+βnP2n(x)+4n+54n+1 γnP2n+2(x).
S=fT(θ, φ)P2(cos β)dΩ+fC(θ, φ)P2(cos β)dΩ.
f˜X(θ, φ)=fX(θ, φ)cos2 β,X=T, C.
S=32 f˜T(θ, φ)dΩ+32 f˜C(θ, φ)dΩ-12.
f˜X(θ)=02πf˜X(θ, φ)dφ,X=T, C,
a˜.n=ACTIΓ˜n23 b0+415 b1-ATCI(ana˜n-1+βna˜n+γna˜n+1)+1τ {2a0Γ˜n-a˜n},
b˜.n=ATCIΓ˜n23 a0+415 a1-ACTI{αnb˜n-1+βnb˜n+γnb˜n+1}+1τ {2b0Γ˜n-b˜n},
Γ˜n=4n+12 02π0πp(θ, φ)cos2 βP2n(cos θ)sin θdθdφ.
S=3(a˜0+b˜0)-12.
an=Γn(0),bn=0,
a˜n=Γ˜n(0),b˜n=0.
S0=3Γ˜0(0)-12.
n2=n02+Nε0 02π0π[αTCfT(θ, φ)+αCTfC(θ, φ)]cos2θ sin θdθdφδ0,γ0
=n02+Nε0 0π[αTCfT(θ)+αCTfC(θ)]cos2 θ sin θdθδ0,
n2=n02+Nε0 02π0π[αTCfT(θ, φ)+αCTfC(θ, φ)]cos2(φ+γ0)sin3 θdθdφδ0,γ0
=n02+N2ε0 0π[αTCfT(θ)+αCTfC(θ)]sin3 θdθδ0,
n2-n2=Nε0 0π[αTCfT(θ)+αCTfC(θ)]P2(θ)sin θdθδ0
=2N5ε0 αTCa1+αCTb1δ0,
Δϕ=πdλP (n-n)=πdN5ε0n¯λP αTCa1+αCTb1δ0,
fT()(θ, φ)=rMC+aNTa+cos2 θ p()(θ, φ),
fC()(θ, φ)=r-1MT+bNCb+cos2 θ p()(θ, φ).
MX=02π0πfX()(θ, φ)cos2 θ sin θdθdφ,X=T, C.
Λx=02π0π p()(θ, φ)x+cos2 θ sin θdθdφ,x=a, b,
NC=11+r Λa(1-bΛb)Λb(1-aΛa),
a1=5r4 3(1-aΛa)(1-bΛb)-Λa(1-bΛb)Λb(1-aΛa)+rΛa(1-bΛb),
b1=54 3(1-aΛa)(1-bΛb)-Λb(1-aΛa)Λb(1-aΛa)+rΛa(1-bΛb).
S=32 Λ˜b(1-aΛa)+rΛ˜a(1-bΛb)Λb(1-aΛa)+rΛa(1-bΛb)-12,
Λ˜x=02π0π p()(θ, φ)x+cos2 θ cos2 β sin θdθdφ, x=a, b.
1x+cos2 θ=n=0 4n+12 cn(x)P2n(cos θ),
Λx=n=0cn(x)Γn(),
Λ˜x=n=0cn(x)Γ˜n().
p(θ, φ)=A exp[-W(θ, φ)],
W=-cP2(cos β)=-c cos2 β+c,
p(θ, φ)=A exp(c cos2 β).
4n+12 02π0π exp(c cos2 β)P2n(cos θ)sin θdθdφ
=P2n(cos δ)Fn(c),
Fn(c)=π(4n+1)-11 exp(cx2)P2n(x)dx=π(4n+1)2n+1k=0cn+k (2k+2n-1)!!k!(2k+4n+1)!!.
F0(c)=π3/2c1/2 ΦI(c1/2).
Γn=P2n(cos δ) Fn(c)2F0(c).
Γ0=12,
Γ1=P2(cos δ) 54 3 exp(c)π1/2c1/2ΦI(c1/2)-1-32c.
p(θ, φ)cos2 β=ddc [p(θ, φ)exp(c cos2 β)]c=0.
Γ˜n=P2n(cos δ) ddc Fn(c+c)2F0(c)c=0
=P2n(cos δ) αnFn-1(c)+βnFn(c)+γnFn+1(c)2F0(c).
S0=F1(c)5F0(c)=12 3 exp(c0S0)π1/2c01/2S01/2ΦI(c01/2S01/2)-1-32c0S0.
d(Δϕ)dtt=0=KI,K=πdN15ε0n¯λP ATCαTC(qS02-1),
Δϕ=3KATC(qS02-1) a1+qb1δ0.
AbsTC(λ)=AbsTC(λTC) γ2(λ-λTC)2+γ2,
AbsTC(λ)=13 ln(10) NσTC(λ)d,
(cos δ0)i=iN,i=0, 1, , N.
(cos δ0)i=iN-3N2(N-1)+i 2N3(N-1)1/2,
i=0,1, , N.

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